Find a Strictly Unimodal Array Peak and Analyze Plateaus

An array strictly increases up to a unique maximum and strictly decreases afterward. Return the index of that peak using binary search. ### Constraints and Clarifications Use a nonempty array of comparable values. As a practice convention, either strictly monotone side may be empty, so the maximum may occur at an endpoint. No numerical bounds are reported. The base contract excludes equal adjacent values. The follow-up asks what changes when equal values are allowed; discuss the assumptions rather than claiming every duplicate-containing array forbids every binary-search method. ### What a Strong Answer Covers Use the slope between adjacent middle elements to discard one side, prove the peak remains in the search interval, and explain why an equality can remove directional information under weaker assumptions. ### Follow-up Questions - Can a weakly unimodal array with arbitrary plateaus guarantee logarithmic peak search? - What extra restriction, such as a plateau only at the maximum, could permit a specialized search?